Dengue, a vector-borne viral disease of increasing global importance, is classically associated with tropical and sub-tropical regions around the world. Urbanisation, globalisation and climate trends, however, are facilitating the geographic spread of its mosquito vectors, thereby increasing the risk of the virus establishing itself in previously unaffected areas and causing large-scale epidemics. On 3 October 2012, two autochthonous dengue infections were reported within the Autonomous Region of Madeira, Portugal. During the following seven months, this first ‘European’ dengue outbreak caused more than 2000 local cases and 81 exported cases to mainland Europe. Here, using an ento-epidemiological mathematical framework, we estimate that the introduction of dengue to Madeira occurred around a month before the first official cases, during the period of maximum influx of airline travel, and that the naturally declining temperatures of autumn were the determining factor for the outbreak's demise in early December 2012. Using key estimates, together with local climate data, we further propose that there is little support for dengue endemicity on this island, but a high potential for future epidemic outbreaks when seeded between May and August—a period when detection of imported cases is crucial for Madeira's public health planning.